Quantum computing with Bianchi groups

Michel Planat; Raymond Aschheim; Marcelo M. Amaral; Klee Irwin

doi:10.1051/epjconf/201919800012

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arXiv · 1808.06831

Quantum computing with Bianchi groups

Michel Planat·Raymond Aschheim·Marcelo M. Amaral·Klee Irwin

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Abstract

It has been shown that non-stabilizer eigenstates of permutation gates are appropriate for allowing $d$-dimensional universal quantum computing (uqc) based on minimal informationally complete POVMs. The relevant quantum gates may be built from subgroups of finite index of the modular group $\Gamma=PSL(2,\mathbb{Z})$ [M. Planat, Entropy 20, 16 (2018)] or more generally from subgroups of fundamental groups of $3$-manifolds [M. Planat, R. Aschheim, M.~M. Amaral and K. Irwin, arXiv 1802.04196(quant-ph)]. In this paper, previous work is encompassed by the use of torsion-free subgroups of Bianchi groups for deriving the quantum gate generators of uqc. A special role is played by a chain of Bianchi congruence $n$-cusped links starting with Thurston's link.

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BibTeX RIS

Michel Planat, Raymond Aschheim, Marcelo M. Amaral, Klee Irwin. 2018-08-21. Quantum computing with Bianchi groups. https://doi.org/10.1051/epjconf%2F201919800012

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